So what's actually in a climber's kit? I seem to remember something about special gloves or some such but I'm probably half-remembering something from a PHB of my youth that might have been 2e or even AD&D.

Notably though, the rules about pitons say that you need to place one every three feet, at one minute a piece in order to get a DC 15 check. I think this is based on a radical misunderstanding of how real-world climbing works and just how many pitons this would mean you need and how much they'd weigh. IRL you use pitons to anchor your ropes, and generally you climb back down and remove them, but it's time-consuming (less so with modern spring-loaded gear of course), and even 20' of hemp rope is heavy. Also, you can't hammer them into a rock face, you place them in appropriate cracks.

But in any case, the point is that a handhold every three feet means you are 3-point anchored while you are carefully hammering in your next piton. This is a far cry from being able to place a dagger into the rock as you leap upwards, and if the adamantine can actually cut the rock like butter, she's got a whole different problem, which is that she needs to somehow place it just right so it doesn't just cut through the rock all the way down to the ground (imagine trying to stop your fall by sticking a knife into a wall of butter...).

I guess what I'm getting at is that even if we accept that the dagger is a good handhold, being able to place the dagger as she does seems like a considerably harder climb check. Or just artistic license, sigh.